Combined Airfoil and Snubber Design Optimization of Turbine Blades With Respect to Friction Damping

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Matthias Hüls ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Turbine Blade ◽  
Contact Force ◽  
Turbine Blades ◽  
Geometric Design ◽  
Torsional Stiffness ◽  
Design Parameters ◽  
System Response ◽  
Friction Damping ◽  
Normal Contact ◽  
Normal Contact Force

A major concern for new generations of large turbine blades is forced and self-excited (flutter) vibrations, which can cause high-cycle fatigue (HCF). The design of friction joints is a commonly applied strategy for systematic reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of geometric blade design parameters onto the damped system response is investigated for direct snubber coupling. A simplified turbine blade geometry is parametrized and a well-proven reduced-order model for turbine blade dynamics under friction damping is integrated into a 3D finite element tool-chain. The developed process is then used in combination with surrogate modeling to predict the effect of geometric design parameters onto the vibrational characteristics. As such, main and interaction effects of design variables onto static normal contact force and resonance amplitudes are determined for a critical first bending mode. Parameters were found to influence the static normal contact force based on their effect on elasticity of the snubber, torsional stiffness of the airfoil and free blade untwist. The results lead to the conclusion that geometric design parameters mainly affect the resonance amplitude equivalent to their influence on static normal contact force in the friction joint. However, it is demonstrated that geometric airfoil parameters influence blade stiffness and are significantly changing the respective mode shapes, which can lead to lower resonance amplitudes despite an increase in static contact loads. Finally, an evolutionary optimization is carried out and novel design guidelines for snubbered blades with friction damping are formulated.

Influence of Geometric Design Parameters Onto Vibratory Response and High-Cycle Fatigue Safety for Turbine Blades With Friction Damper

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Matthias Hüls ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
High Cycle Fatigue ◽  
Turbine Blades ◽  
Geometric Design ◽  
Design Parameters ◽  
System Response ◽  
Blade Design ◽  
Cycle Fatigue ◽  
Friction Damping ◽  
Damped System ◽  
Vibratory Response

Among the major concerns for high aspect-ratio, turbine blades are forced and self-excited (flutter) vibrations, which can cause failure by high-cycle fatigue (HCF). The introduction of friction damping in turbine blades, such as by coupling of adjacent blades via under platform dampers, can lead to a significant reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of basic geometric blade design parameters onto the damped system response will be investigated to link design parameters with functional parameters like damper normal load, frequently used in nonlinear dynamic analysis. The shape of a simplified turbine blade is parameterized along with the under platform damper configuration. The airfoil is explicitly included into the parameterization in order to account for changes in blade mode shapes. For evaluation of the damped system response, a reduced-order model for nonlinear friction damping is included into an automated three-dimensional (3D) finite element analysis (FEA) tool-chain. Based on a design of experiments approach, the design space will be sampled and surrogate models will be trained on the received dataset. Subsequently, the mean and interaction effects of the geometric design parameters onto the resonance amplitude and safety against HCF will be outlined. The HCF safety is found to be affected by strong secondary effects onto static and resonant vibratory stress levels. Applying an evolutionary optimization algorithm, it is shown that the optimum blade design with respect to minimum vibratory response can differ significantly from a blade designed toward maximum HCF safety.

Optimization of Supersonic Axial Turbine Blades Based on Surrogate Models

2020 ◽  
Author(s):  
Markus Waesker ◽  
Bjoern Buelten ◽  
Norman Kienzle ◽  
Christian Doetsch
Keyword(s):  
Reynolds Number ◽  
Turbine Blade ◽  
Surrogate Model ◽  
Cfd Simulation ◽  
Turbine Blades ◽  
Energy System ◽  
Design Parameters ◽  
Blade Design ◽  
Axial Turbine ◽  
Velocity Coefficient

Abstract Due to the transition of the energy system to more decentralized sector-coupled technologies, the demand on small, highly efficient and compact turbines is steadily growing. Therefore, supersonic impulse turbines have been subject of academic research for many years because of their compact and low-cost conditions. However, specific loss models for this type of turbine are still missing. In this paper, a CFD-simulation-based surrogate model for the velocity coefficient, unique incidence as well as outflow deviation of the blade, is introduced. This surrogate model forms the basis for an exemplary efficiency optimization of the “Colclough cascade”. In a first step, an automatic and robust blade design methodology for constant-channel blades based on the supersonic turbine blade design of Stratford and Sansome is shown. The blade flow is fully described by seven geometrical and three aerodynamic design parameters. After that, an automated numerical flow simulation (CFD) workflow for supersonic turbine blades is developed. The validation of the CFD setup with a published supersonic axial turbine blade (Colclough design) shows a high consistency in the shock waves, separation zones and boundary layers as well as velocity coefficients. A design of experiments (DOE) with latin hypercube sampling and 1300 sample points is calculated. This CFD data forms the basis for a highly accurate surrogate model of supersonic turbine blade flow suitable for Mach numbers between 1.1 and 1.6. The throat-based Reynolds number is varied between 1*104 and 4*105. Additionally, an optimization is introduced, based on the surrogate model for the Reynolds number and Mach number of Colclough and no degree of reaction (equal inlet and outlet static pressure). The velocity coefficient is improved by up to 3 %.

Experimental Validation of a Volumetric Planetary Rover Wheel/Soil Interaction Model

2013 ◽  
Author(s):  
Willem Petersen ◽  
John McPhee
Keyword(s):  
Contact Force ◽  
Interaction Model ◽  
Contact Model ◽  
Soil Parameters ◽  
Model Parameters ◽  
Force Model ◽  
Normal Contact ◽  
Planetary Rover ◽  
Normal Contact Force ◽  
Contact Force Model

For the multibody simulation of planetary rover operations, a wheel-soil contact model is necessary to represent the forces and moments between the tire and the soft soil. A novel nonlinear contact modelling approach based on the properties of the hypervolume of interpenetration is validated in this paper. This normal contact force model is based on the Winkler foundation model with nonlinear spring properties. To fully define the proposed normal contact force model for this application, seven parameters are required. Besides the geometry parameters that can be easily measured, three soil parameters representing the hyperelastic and plastic properties of the soil have to be identified. Since it is very difficult to directly measure the latter set of soil parameters, they are identified by comparing computer simulations with experimental results of drawbar pull tests performed under different slip conditions on the Juno rover of the Canadian Space Agency (CSA). A multibody dynamics model of the Juno rover including the new wheel/soil interaction model was developed and simulated in MapleSim. To identify the wheel/soil contact model parameters, the cost function of the model residuals of the kinematic data is minimized. The volumetric contact model is then tested by using the identified contact model parameters in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain and compared against experiments.

A Study of Optimization of Blade Section Shape for a Steam Turbine

2005 ◽  
Author(s):  
Kyung-Nam Chung ◽  
Yang-Ik Kim ◽  
Ju-Heon Sung ◽  
In-Ho Chung ◽  
Sang-Hoon Shin
Keyword(s):  
Turbine Blade ◽  
Optimization Design ◽  
Design Method ◽  
Turbine Blades ◽  
Design Parameters ◽  
Surface Model ◽  
Impulse Turbine ◽  
Object Function ◽  
Section Shape ◽  
Blade Section

In this study, an optimization design method is established for a rotor blade of a Curtis turbine. Bezier curve is generally used to define the profile of turbine blades. However, this curve is not proper to a supersonic impulse turbine. Section shape of a supersonic turbine blade is composed of straight lines and circular arcs. That is, it has several constraints to define the section shape. Thus, in this study, a blade design method is developed by using B-spline curve in which local control is possible. The turbine blade section has been changed by varying three design parameters of exit blade angle, stagger angle and maximum camber. Then flow analyses have been carried out for the sections. Lift-drag ratio of the blade section is used as the object function, and it is maximized in the optimization. Second-order response surface model is employed to express the object function as a function of design parameters. Central composite design method is used to reduce the number of design points. Then, an evolution strategy is employed to obtain the optimized section of the Curtis turbine blade.

Shape Optimal Design of Contact Springs of Electronic Connectors

2002 ◽  
Vol 124 (3) ◽  
pp. 178-183 ◽  
Author(s):  
Yeh-Liang Hsu ◽  
Yuan-Chan Hsu ◽  
Ming-Sho Hsu
Keyword(s):  
Contact Force ◽  
Printed Circuit Boards ◽  
Normal Force ◽  
Optimization Techniques ◽  
Contact Forces ◽  
Design Parameters ◽  
Original Design ◽  
Insertion Force ◽  
Element Analysis ◽  
Normal Contact

An electronic connector provides a separable interface between two subsystems of an electronic system. The contact spring is probably the most critical component in an electronic connector. Mechanically, the contact spring provides the contact normal force, which establishes the contact interface as the connector is mated. However, connector manufacturers have a basic struggle between the need for high normal contact forces and low insertion forces. Designing connectors with large numbers of pins that are used with today’s integrated circuits and printed circuit boards often results in an associated rise in connector insertion force. It is possible to lower the insertion force of a connector by redesigning the geometry of the contact spring, but this also means a decrease in contact normal force. In this paper, structural shape optimization techniques are used to find the optimal shape of the contact springs of an electronic connector. The process of the insertion of a PCB into the contact springs of a connector is modeled by finite element analysis. The maximum insertion force and the contact normal force are calculated. The effects of several design parameters are discussed. The geometry of the contact springs is then parameterized and optimized. The required insertion force is minimized while the normal contact force and the resulting stress are maintained within specified values. In our example, the insertion force of the final contact spring design is reduced to 68.3% of that of the original design, while the contact force and the maximum stress are maintained within specified values.

A Theoretical Model for the Normal Contact Force of Two Elastoplastic Ellipsoidal Bodies

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Verena Becker ◽  
Marc Kamlah
Keyword(s):  
Theoretical Model ◽  
Contact Force ◽  
General Description ◽  
Element Analysis ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Static Contact ◽  
Elliptical Contact ◽  
Individual Grains ◽  
Force Displacement

Abstract To model the mechanical behavior of granular materials, a reliable description of the material properties is indispensable. Individual grains are usually not perfectly spherical. In batteries, for instance, lithium nickel manganese cobalt oxide (NMC) is a frequently used material, consisting out of particles with possibly ellipsoidal like shapes. As particles may plastically deform under increasing stresses, the paper presents a theoretical model for the normal contact force of elastoplastic ellipsoidal bodies for the use in the context of mechanical discrete element method (DEM). The model can be considered as extension of the elastic, elastic-plastic, fully plastic Thornton model by using a more general description to incorporate elliptical contact areas. The focus is on a normal contact force description as continuous function of time for all regimes, elastic, elastoplastic, and fully plastic loading, as well as unloading from elastoplastic loading, while the evolution of the plastic contact area is not considered here. All underlying formulae to describe the force-displacement relationship for the static contact problem are derived, partly based on finite element analysis (FEA). To verify the new model, FEAs are performed and their results compared with the model predictions.

Normal and Angular Motions at Rough Planar Contacts During Sliding With Friction

1992 ◽  
Vol 114 (3) ◽  
pp. 567-578 ◽  
Author(s):  
D. P. Hess ◽  
A. Soom
Keyword(s):  
Nonlinear Equations ◽  
Contact Force ◽  
Contact Area ◽  
Normal Contact ◽  
Frictional Contacts ◽  
Normal Contact Force ◽  
The Real ◽  
Real Area Of Contact ◽  
Real Area ◽  
Contact Vibrations

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Influence of Geometric Design Parameters Onto Vibratory Response and HCF Safety for Turbine Blades With Friction Damper

2018 ◽  
Author(s):  
Matthias Hüls ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Aspect Ratio ◽  
High Cycle Fatigue ◽  
Turbine Blades ◽  
Design Parameters ◽  
System Response ◽  
Blade Design ◽  
Cycle Fatigue ◽  
Resonance Amplitude ◽  
Damped System ◽  
Vibratory Response

Among the major concerns for high aspect-ratio turbine blades are forced and self-excited (flutter) vibrations which can cause failure by high-cycle fatigue. The introduction of friction damping in turbine blades, such as by coupling of adjacent blades via under platform dampers, can lead to a significant reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of basic geometric blade design parameters onto the damped system response will be investigated to link design parameters with functional parameters like damper normal load, frequently used in nonlinear dynamic analysis. The shape of a simplified large aspect-ratio turbine blade is parameterized along with the under platform damper configuration. The airfoil is explicitly included into the parameterization in order to account for changes in blade mode shapes. For evaluation of the damped system response under a typical excitation, a reduced order model for non-linear friction damping is included into an automated 3D FEA tool-chain. Based on a design of experiments approach, the design space will be sampled and a surrogate model is trained on the received dataset. Subsequently, the mean and interaction effects of the true geometric blade design parameters onto the resonance amplitude and safety against high-cycle fatigue will be outlined for a critical first bending type vibrational motion. Design parameters were mainly found to influence the resonance amplitude by their effect onto the tip-to-platform deflection ratio. The HCF safety was affected by those design parameters with large sensitivity onto static and resonant vibratory stress levels. Applying an evolutionary optimization algorithm, it is shown that the optimum blade design with respect to minimum vibratory response at a particular node can differ significantly from a blade designed toward maximum HCF safety.

Elastic-Plastic Finite-Element Analysis of Repeated, Two-Dimensional Wheel-Rail Rolling Contact under Time-Dependent Load

2006 ◽  
Vol 220 (5) ◽  
pp. 603-613 ◽  
Author(s):  
Z. F. Wen ◽  
X. S. Jin
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Contact Force ◽  
Rolling Contact ◽  
Time Dependent ◽  
Two Dimensional ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Residual Strains ◽  
Harmonic Variation

A study was performed using a finite-element model to obtain stresses, strains, and deformations for repeated, two-dimensional rolling contact of a locomotive driving wheel and a rail under time-dependent load. An advanced cyclic plasticity model was used with a commercial finite element code via a material subroutine. The time-dependent load was considered a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was assumed to follow the Hertzian distribution and the tangential force followed the Carter distribution. A wavy profile is formed on the running surface of the rail subjected to the harmonic variation of the normal (vertical) contact force. The developed wavelength of the profile corresponds to the frequency of the normal contact force for the actual train speed. The creepage or rolling-sliding condition plays an important role in the residual strains and deformations, but its influence on the residual stresses is insignificant. The residual stresses at the surface decrease with increasing rolling passes and gradually tend to stabilize. The residual strains and surface displacements increase with increasing rolling cycle, but the increases in residual strain and surface displacement per rolling pass (ratchetting rate) decay. The residual stresses, strains, and deformations near the wave trough of the residual wavy deformation are larger than those near the wave crest. For any given creepage including zero value, when the number of rolling passes increases, the surface depth of the wavy-deformed surface increases but the ratchetting rate decays. The results are useful in investigating the influence of plastic deformation on rail corrugation.

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